The former Leeds United chairman joined the Ninian Park side as a consultant in March on a three-month contract to help tackle the club's £30m debts.
Former chief executive David Temme is now in charge of Cardiff's new stadium project, which owner Sam Hammam describes as "the single most important and strategic activity that we have to manage".
Terry Burton and the rest of the back-room staff will remain at the club.
It is believed that once the stadium project is well under-way and close to completion that the financial problems at Cardiff will subside, however, that project still seems far from being completed.